In the theory of special relativity one encounters the notion of time dilatation. A commonly cited example is that “a clock moving relative to an observer is found to run more slowly than one at rest relative to him” [1]. This concept, although readily acceptable on a purely mathematical basis, often appears somewhat mystical to a student, when compared with his everyday experiences in the physical world. In order to bridge the gap between the mathematics and the physical world, a simple physical analogy (which could easily be constructed as a classroom demonstration) illustrates in a nonrelativistic manner this rather unintuitive notion of relativistic time dilatation.